# Valuing a floating-rate bond [duplicate]

Suppose we have a floating-rate bond with arbitrary face value.

I am given to understand that the value of such a bond is the face value, at the time it is issued and also after each coupon payment.

As an example, let the face value be 100, and let the interest rate at the time of issuance be 5%, so the coupon payment at the end of the first period is 5. Hence, the value of the bond is: $$\frac{(100 +5)}{1.05}=100$$

A couple of things: 1. Why do we only consider the first period? Does this assume the bond is callable? 2. Do we assume the discount rate is the same as the floating rate?